I've seen all of these "proofs" being added recently for 2 = 0, 1 < 0, etc, etc...so I figured I'd add my two proofs for 2 = 1, and proof that magic exists...

I apologize if these have already been posted...I haven't seen them yet though, so I thought I would put them up. These aren't difficult, and I fully expect them to be solved very quickly, but they're fun.

This first one is the golden oldie (I learned this one quite a few years ago and still like it):

let a = b

a^{2} = ab (multiply both sides by a)

a^{2} - b^{2} = ab - b^{2}(subtract b^{2} from both sides)

(a + b)(a - b) = b(a - b) (factor)

(a + b) = b (divide both sides by (a - b) )

b + b = b (substitution)

2b = b

2 = 1

Then this following one uses calculus (fun one at first when learning calculus):

x = 1 + 1 + ... + 1 (x times)

x^{2} = x + x + ... + x (multiply through by x)

2x dx = (1 + 1 + ... + 1) dx (take deriviative of both sides)

2x = (1 + 1 + ... + 1)

2x = x

2 = 1

and my last one is to show that something TRULY can come from nothing:

## Question

## Pickett 13

I've seen all of these "proofs" being added recently for 2 = 0, 1 < 0, etc, etc...so I figured I'd add my two proofs for 2 = 1, and proof that magic exists...

I apologize if these have already been posted...I haven't seen them yet though, so I thought I would put them up. These aren't difficult, and I fully expect them to be solved very quickly, but they're fun.

This first one is the golden oldie (I learned this one quite a few years ago and still like it):

let a = b

a

^{2}= ab(multiply both sides by a)a

^{2}- b^{2}= ab - b^{2}(subtract b^{2}from both sides)(a + b)(a - b) = b(a - b)

(factor)(a + b) = b

(divide both sides by (a - b) )b + b = b

(substitution)2b = b

2 = 1

Then this following one uses calculus (fun one at first when learning calculus):

x = 1 + 1 + ... + 1

(x times)x

^{2}= x + x + ... + x(multiply through by x)2x dx = (1 + 1 + ... + 1) dx

(take deriviative of both sides)2x = (1 + 1 + ... + 1)

2x = x

2 = 1

and my last one is to show that something TRULY can come from nothing:

0 = 0 + 0 + 0 + ...

0 = (1 - 1) + (1 - 1) + (1 - 1) + ...

(since 0 = 1 - 1)0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ...

(associative law of addition)0 = 1 + 0 + 0 + 0 + ...

(since -1 + 1 = 0)0 = 1

So, as if by magic something appeared out of nothing! YAY!

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